• Journal of applied mathematics & informatics
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• 제20권1_2호
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• pp.293-303
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• 2006

This paper describes a numerical scheme for optimal control of a time-dependent linear system to a moving final state. Discretization of the corresponding differential equations gives rise to a linear algebraic system. Defining some binary variables, we approximate the original problem by a mixed integer linear programming (MILP) problem. Numerical examples show that the resulting method is highly efficient.

• 산업경영시스템학회지
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• 제14권23호
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• pp.1-6
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• 1991

The physical distribution service(PDS) is essential to evaluate the business logistics system. The PDS combines the inventory service with the lead time to deliver. This paper is presented to model Mixed Zero-One integer programming which is to determine distribution center location and to allocation products, considering delivery lead time, from given candidate locations to given customer markets. A numerical example is given to demonstrate the applicability of Mixed Zero-One integer programming for Distribution-Location problem.

• Journal of applied mathematics & informatics
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• 제19권1_2호
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• pp.371-384
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• 2005

Usual symmetric duality results are proved for Wolfe and Mond-Weir type nondifferentiable nonlinear symmetric dual programs under F-convexity F-concavity and F-pseudoconvexity F-pseudoconcavity assumptions. These duality results are then used to formulate Wolfe and Mond-Weir type nondifferentiable minimax mixed integer dual programs and symmetric duality theorems are established. Moreover, nondifferentiable fractional symmetric dual programs are studied by using the above programs.

• 경영과학
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• 제33권2호
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• pp.75-87
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• 2016

Quality function deployment (QFD) is a widely adopted customer-oriented product development methodology by analyzing customer requirements. It is a main activity in QFD planning process to determine the optimal values of the technical attributes (TAs) so as to achieve the customer requirements (CRs) from the House of Quality (HoQ). In most of the previous research, all the TAs in QFD are assumed to have either continuous or discrete values. In the real world applications, the continuous TAs and the discrete TAs are often mixed in QFD. In this paper, a mixed integer linear programming model is formulated to obtain the optimal values for the continuous TAs and the discrete TAs in QFD planning as well as Branch and Bound (B and B) algorithm is proposed as the solution approach. Finally, the proposed model and solution approach are illustrated with an office chair under multi-segment market, and the sensitivity analysis is performed to study how the proposed model and its solutions respond to the variation for the two elements which are budget and CRs' weights.

• 한국항해학회지
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• 제22권4호
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• pp.15-19
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• 1998

This paper concerns a bulk or semibulk cargo ship scheduling problem with a single loading port. This type of ship scheduling problem is frequently needed in real world for carrying minerals or agricultural produce from a major single production zone to many destinations scattered over a large area of the world. The first optimization model for this problem was introduced by Ronen (1986) as a nonlinear mixed integer program. The model developed in this paper is an improvement of his model in the sense that nonlinearities and numerous unnecessary integer variables have been eliminated. By this improvement we could expect real world instances of moderate sizes to be solved optimal solutions by commercial integer programming software. Similarity between the ship scheduling model and the capacitated facility location model is also discussed.

• 산업경영시스템학회지
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• 제44권1호
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• pp.26-36
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• 2021

The topic of this study is the field of humanitarian logistics for disaster response. Many existing studies have revealed that compliance with the golden time in response to a disaster determines the success or failure of relief activities, and logistics costs account for 80% of the disaster response cost. Besides, the agility, responsiveness, and effectiveness of the humanitarian logistics system are emphasized in consideration of the disaster situation's characteristics, such as the urgency of life-saving and rapid environmental changes. In other words, they emphasize the importance of logistics activities in disaster response, which includes the effective and efficient distribution of relief supplies. This study proposes a mathematical model for establishing a transport plan to distribute relief supplies in a disaster situation. To determine vehicles' route and the amount of relief for cities suffering a disaster, it mainly considers the urgency, effectiveness (restoration rate), and uncertainty in the logistics system. The model is initially developed as a mixed-integer nonlinear programming (MINLP) model containing some nonlinear functions and transform into a Mixed-integer linear programming (MILP) model using a logarithmic transformation and piecewise linear approximation method. Furthermore, a minimax problem is suggested to search for breakpoints and slopes to define a piecewise linear function that minimizes the linear approximation error. A numerical experiment is performed to verify the MILP model, and linear approximation error is also analyzed in the experiment.

• 전기학회논문지
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• 제67권7호
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• pp.833-839
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• 2018

This paper presents an analysis and the methodology of optimal operation strategy of the ESS(Energy Storage System) for reduce electricity charges. Electricity charges consist of a basic charge based on the contract capacity and energy charge according to the power usage. In order to use electrical energy at minimal charge, these two factors are required to be reduced at the same time. QP(Quadratic Programming) is appropriate for minimization of the basic charge and LP(Linear Programmin) is adequate to minimize the energy charge. However, the integer variable have to be introduced for modelling of different charge and discharge efficiency of ESS PCS(Power Conversion System), where MILP(Mixed Integer Linear Programming) can be used. In this case, the extent to which the peak load savings is accomplished should be assumed before the energy charge is minimized. So, to minimize the electricity charge exactly, optimization is sequentially performed in this paper, so-called the Two Stage Hybird optimization, where the extent to which the peak load savings is firstly accomplished through optimization of basic charge and then the optimization of energy charge is performed with different charge and discharge efficiency of ESS PCS. Finally, the proposed method is analyzed quantitatively with other optimization methods.

• 한국컴퓨터정보학회논문지
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• 제26권12호
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• pp.255-264
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• 2021

본 연구에서는 부유식 해상풍력발전의 운영 및 유지보수에 필요한 체계적인 정비계획 수립을 위해 최적화기법을 활용한 수리 모형을 제안하고자 한다. 주간 단위로 선박과 기술자를 운용하는 계획정비와 고장정비 작업의 배정에 혼합정수계획법(Mixed Integer Linear Programming, MILP)을 도입하였다. 본 연구의 최적화 모델을 활용한 사례연구에서는 선박과 기술자의 투입 규모가 유지정비 비용에 미치는 영향을 확인하였으며 1년간 정비계획 수립에서 더 나아가 정비작업별 상세 스케줄링까지 연계되는 단계적 최적화 방법론을 함께 제시하였다. 세부적으로는 기상 데이터와 정비 데이터를 활용한 발전량 손실을 비가동 비용으로 반영하여 정비 우선순위를 선정하였으며, 이를 통해 국내 실정에 맞는 해상풍력단지의 유지보수 전략을 제시할 수 있을 것으로 기대한다.

• 조명전기설비학회논문지
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• 제16권5호
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• pp.75-82
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• 2002

본 논문에서는 열병합발전설비의 최적운용계획을 위한 새로운 수리적 모델을 제안하였다. 본 논문에서 제안한 알고리즘은 에너지생산량에 따른 비용의 비선형적인 문제를 구간별로 선형화된 함수를 이용하여 혼합정수 계획법으로 모델링하였다. 제안한 수리적 모델은 종래 제시되었던 열병합발전설비의 최적운용을 위한 모델링 기법에서 해결하지 못했던 한계사항을 극복한 것으로서, 더욱 현실에 근접한 최적운용을 위한 모델이 되었다. 또한 본 연구에서는 시뮬레이션을 통해 다양한 사례에 대한 열병합발전설비의 최적 운용계획을 제시함으로서 수리적 모델의 유용성을 입증하였다.

• 대한산업공학회지
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• 제31권4호
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• pp.265-276
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• 2005

ELECTRE IS requires the decision maker (DM) to specify several parameters such as weights, pseudo-criteria thresholds and the concordance level. Among these parameters, the concordance level has a significant effect on the outranking relation. And the number of alternatives selected may be sensitive to the value of these parameters. Therefore the DM may have to perform many iterations to obtain the desired number of alternatives in the kernel set. In this study, we developed a mixed-integer programming (MIP) model to elicit the concordance level and thereby to choose the desired number of alternatives in the kernel set. The MIP model can be applied in the interactive process so that the pseudo-criteria thresholds are adjusted according to the results of MIP model. Using the MIP model in the interactive process, we can reduce the number of iterations needed to perform ELECTRE IS.